1. **State the problem:** We need to estimate the air density $\rho$ in kg/m³ given the air temperature $T = 15^\circ C$, pressure $P = 1008$ hPa, and gas constant $R = 287$ J kg⁻¹ K⁻¹ using the ideal gas law. 2. **Convert units:** - Temperature must be in Kelvin: $$T = 15 + 273.15 = 288.15\ K$$ - Pressure must be in Pascals (Pa): $$P = 1008\ hPa = 1008 \times 100 = 100800\ Pa$$ 3. **Recall the ideal gas law for density:** $$\rho = \frac{P}{R T}$$ where $\rho$ is density, $P$ is pressure, $R$ is the specific gas constant, and $T$ is temperature in Kelvin. 4. **Substitute values:** $$\rho = \frac{100800}{287 \times 288.15}$$ 5. **Calculate denominator:** $$287 \times 288.15 = 82675.05$$ 6. **Calculate density:** $$\rho = \frac{100800}{82675.05} \approx 1.219\ kg/m^3$$ 7. **Round to nearest hundredth:** $$\rho \approx 1.22\ kg/m^3$$ **Final answer:** The estimated air density is **1.22 kg/m³**.